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Properties of Decomposition Operators of Spline-Wavelet Decompositions

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We consider second order spline-wavelet decompositions and prove that the decomposition operators are independent of the order of removing certain grid nodes. We introduce the notion of a k-localized system of functionals and extract the set of operators containing only one left inverse of an embedding operator. Bibliography: 3 titles.

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References

  1. Yu. K. Dem’yanovich and O. M. Kosogorov, “Calibration relations for nonpolynomial splines” [in Russian], Probl. Mat. Anal. 43, 51–67 (2009); English transl.: J. Math. Sci., New York 164, No. 3, 364– 382 (2010).

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  2. Yu. K. Dem’yanovich, “Nonsmooth spline-wavelet ewxpansions and their properties” [in Russian] Zap. Nauchn. Semin. POMI 395, 31–60 (2011); English transl.: J. Math. Sci., New York 182, No 6, 761–768 (2012).

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  3. Yu. K. Dem’yanovich, Theory of Spline Wavelets [in Russian], St. Peteresb. State Univ. Press, St. Petersb. (2013).

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Authors and Affiliations

  1. St. Petersburg State University, 28, Universitetskii pr., Petrodvorets, St. Petersburg, 198504, Russia

    Yu. K. Dem’yanovich & I. G. Burova

Authors
  1. Yu. K. Dem’yanovich
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  2. I. G. Burova
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Correspondence to Yu. K. Dem’yanovich.

Additional information

Translated from Problemy Matematicheskogo Analiza 77, December 2014, pp. 77-90.

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Dem’yanovich, Y.K., Burova, I.G. Properties of Decomposition Operators of Spline-Wavelet Decompositions. J Math Sci 205, 205–221 (2015). https://doi.org/10.1007/s10958-015-2242-7

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  • DOI: https://doi.org/10.1007/s10958-015-2242-7

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